The regular graph on n points with degree n-1 is denoted Kn. In other words, every point is connected to every other point. This is also called a complete graph.
A bipartite graph has two sets of vertices, with edges connecting the two sets, and no edges internal to either set. A graph is bipartite iff every circuit has even length.
The graph Km,n is a complete bipartite graph, with all m points connected to all n points. The number of vertices is m+n, and the number of edges is mn.